As a junior, Pospíšilová was a member of the Czechoslovak team which won the 1986 World Youth Cup in Japan and she was runner-up to Natasha Zvereva in the girls' singles at the 1987 French Open.

When Czechoslovakia won the competition in 1988, Pospíšilová featured in all five World Group matches, as the doubles partner of Jana Novotná.

The pair were unbeaten until losing in the final to the USSR, but Czechoslovakia had already secured the title after winning both singles matches.

In her first season she had a win over second-seeded Helena Suková in a match at the 1988 European Indoors and lost the final of the Southern Cross Classic to Fed Cup teammate Jana Novotná, to finish at 50th in the year-end rankings.

At the 1990 Athens Trophy, Pospíšilová partnered with Leona Lásková to reach her only career doubles final.